If the file is moved (in the same filesystem) or renamed, then the file handle remains open and can still be used to read and write the file.
If the file is deleted, the file handle remains open and can still be used (This is not what some people expect). The file will not really be deleted until the last handle is closed.
If the file is replaced by a new file, it depends exactly how. If the file’s contents are overwritten, the file handle will still be valid and access the new content. If the existing file is unlinked and a new one created with the same name or, if a new file is moved onto the existing file using rename(), it’s the same as deletion (see above) – that is, the file handle will continue to refer to the original version of the file.
In general, once the file is open, the file is open, and nobody changing the directory structure can change that – they can move, rename the file, or put something else in its place, it simply remains open.
In Unix there is no delete, only unlink(), which makes sense as it doesn’t necessarily delete the file – just removes the link from the directory.
If on the other hand the underlying device disappears (e.g. USB unplug) then the file handle won’t be valid any more and is likely to give IO/error on any operation. You still have to close it though. This is going to be true even if the device is plugged back in, as it’s not sensible to keep a file open in this case.